Hello and thank you for the question.Answers given are for informational purposes only and are not meant to replace an exam by an in-person.I am Dr. Sohaib, a practicing Internal Medicine Specialist and i will do my best to help you today.
The kind of radiating pain you have described (associated with numbness) is most likely a result of a "Pinched Nerve", a condition in which there is abnormal excessive pressure over the nerve anywhere its course. It could be in the spine (due to disc prolapse, cervical spondylosis, vertebral degeneration) or at the shoulder joint.
In this situation, i would recommend MRI of the spine and shoulder to exactly determine the underlying cause, which will clearly define further management plan in specific terms.
If not done now, i fear that your pain might get worse, and an appropriate intervention may be delayed (which eventually would be required along with MRI if the pain does not improve now).
So better have it done now than later.
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Thank you and get well soon :)